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9fd2d2c382
The macros Status, Convex, Opposite, FillSolid (coming from X11 headers) are now undefined in place of definition of methods with same name in OCCT headers. The usage of variables with name Status is now avoided. GL_GLEXT_LEGACY is now defined only if not already defined. The macros AddPrinter (coming from WinAPI headers) is now undefined within Message_Messenger class definition having method with the same name. CurrentDirectory macro is now undefined in OSD_Process.hxx.
1491 lines
49 KiB
Plaintext
1491 lines
49 KiB
Plaintext
// Copyright (c) 1995-1999 Matra Datavision
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// Copyright (c) 1999-2014 OPEN CASCADE SAS
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//
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// This file is part of Open CASCADE Technology software library.
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//
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// This library is free software; you can redistribute it and/or modify it under
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// the terms of the GNU Lesser General Public License version 2.1 as published
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// by the Free Software Foundation, with special exception defined in the file
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// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
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// distribution for complete text of the license and disclaimer of any warranty.
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//
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// Alternatively, this file may be used under the terms of Open CASCADE
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// commercial license or contractual agreement.
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// xab : modified 15-Mar-94 added EvalBSplineMatrix, FactorBandedMatrix, SolveBandedSystem
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// Eval, BuildCache, cacheD0, cacheD1, cacheD2, cacheD3, LocalMatrix,
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// EvalPolynomial, RationalDerivatives.
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// xab : 22-Mar-94 : fixed rational problem in BuildCache
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// xab : 12-Mar-96 : added MovePointAndTangent
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#include <TColStd_Array1OfInteger.hxx>
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#include <TColStd_Array1OfReal.hxx>
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#include <TColStd_Array2OfReal.hxx>
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#include <gp_Vec2d.hxx>
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#include <Standard_ConstructionError.hxx>
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#include <PLib.hxx>
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#include <math_Matrix.hxx>
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//=======================================================================
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//struct : BSplCLib_DataContainer
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//purpose: Auxiliary structure providing buffers for poles and knots used in
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// evaluation of bspline (allocated in the stack)
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//=======================================================================
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struct BSplCLib_DataContainer
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{
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BSplCLib_DataContainer(Standard_Integer Degree)
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{
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(void)Degree; // avoid compiler warning
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Standard_OutOfRange_Raise_if (Degree > BSplCLib::MaxDegree() ||
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BSplCLib::MaxDegree() > 25,
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"BSplCLib: bspline degree is greater than maximum supported");
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}
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Standard_Real poles[(25+1)*(Dimension_gen+1)];
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Standard_Real knots[2*25];
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Standard_Real ders[Dimension_gen*4];
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};
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//=======================================================================
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//function : Reverse
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//purpose :
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//=======================================================================
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void BSplCLib::Reverse(Array1OfPoints& Poles,
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const Standard_Integer L)
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{
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Standard_Integer i, l = L;
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l = Poles.Lower() + (l-Poles.Lower()) % (Poles.Upper()-Poles.Lower()+1);
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Array1OfPoints temp(0,Poles.Length()-1);
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for (i = Poles.Lower(); i <= l; i++)
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temp(l-i) = Poles(i);
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for (i = l+1; i <= Poles.Upper(); i++)
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temp(l-Poles.Lower()+Poles.Upper()-i+1) = Poles(i);
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for (i = Poles.Lower(); i <= Poles.Upper(); i++)
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Poles(i) = temp(i-Poles.Lower());
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}
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//
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// CURVES MODIFICATIONS
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//
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//=======================================================================
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//function : RemoveKnot
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//purpose :
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//=======================================================================
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Standard_Boolean BSplCLib::RemoveKnot
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(const Standard_Integer Index,
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const Standard_Integer Mult,
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const Standard_Integer Degree,
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const Standard_Boolean Periodic,
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const Array1OfPoints& Poles,
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const TColStd_Array1OfReal* Weights,
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const TColStd_Array1OfReal& Knots,
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const TColStd_Array1OfInteger& Mults,
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Array1OfPoints& NewPoles,
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TColStd_Array1OfReal* NewWeights,
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TColStd_Array1OfReal& NewKnots,
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TColStd_Array1OfInteger& NewMults,
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const Standard_Real Tolerance)
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{
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Standard_Boolean rational = Weights != NULL;
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Standard_Integer dim;
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dim = Dimension_gen;
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if (rational) dim++;
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TColStd_Array1OfReal poles(1,dim*Poles.Length());
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TColStd_Array1OfReal newpoles(1,dim*NewPoles.Length());
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if (rational) PLib::SetPoles(Poles,*Weights,poles);
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else PLib::SetPoles(Poles,poles);
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if (!RemoveKnot(Index,Mult,Degree,Periodic,dim,
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poles,Knots,Mults,newpoles,NewKnots,NewMults,Tolerance))
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return Standard_False;
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if (rational) PLib::GetPoles(newpoles,NewPoles,*NewWeights);
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else PLib::GetPoles(newpoles,NewPoles);
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return Standard_True;
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}
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//=======================================================================
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//function : InsertKnots
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//purpose : insert an array of knots and multiplicities
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//=======================================================================
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void BSplCLib::InsertKnots
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(const Standard_Integer Degree,
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const Standard_Boolean Periodic,
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const Array1OfPoints& Poles,
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const TColStd_Array1OfReal* Weights,
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const TColStd_Array1OfReal& Knots,
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const TColStd_Array1OfInteger& Mults,
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const TColStd_Array1OfReal& AddKnots,
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const TColStd_Array1OfInteger* AddMults,
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Array1OfPoints& NewPoles,
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TColStd_Array1OfReal* NewWeights,
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TColStd_Array1OfReal& NewKnots,
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TColStd_Array1OfInteger& NewMults,
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const Standard_Real Epsilon,
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const Standard_Boolean Add)
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{
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Standard_Boolean rational = Weights != NULL;
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Standard_Integer dim;
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dim = Dimension_gen;
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if (rational) dim++;
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TColStd_Array1OfReal poles(1,dim*Poles.Length());
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TColStd_Array1OfReal newpoles(1,dim*NewPoles.Length());
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if (rational) PLib::SetPoles(Poles,*Weights,poles);
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else PLib::SetPoles(Poles,poles);
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InsertKnots(Degree,Periodic,dim,poles,Knots,Mults,
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AddKnots,AddMults,newpoles,NewKnots,NewMults,Epsilon,Add);
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if (rational) PLib::GetPoles(newpoles,NewPoles,*NewWeights);
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else PLib::GetPoles(newpoles,NewPoles);
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}
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//=======================================================================
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//function : InsertKnot
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//purpose :
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//=======================================================================
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void BSplCLib::InsertKnot(const Standard_Integer ,
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const Standard_Real U,
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const Standard_Integer UMult,
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const Standard_Integer Degree,
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const Standard_Boolean Periodic,
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const Array1OfPoints& Poles,
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const TColStd_Array1OfReal* Weights,
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const TColStd_Array1OfReal& Knots,
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const TColStd_Array1OfInteger& Mults,
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Array1OfPoints& NewPoles,
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TColStd_Array1OfReal* NewWeights)
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{
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TColStd_Array1OfReal k(1,1);
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k(1) = U;
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TColStd_Array1OfInteger m(1,1);
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m(1) = UMult;
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TColStd_Array1OfReal nk(1,Knots.Length()+1);
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TColStd_Array1OfInteger nm(1,Knots.Length()+1);
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InsertKnots(Degree,Periodic,Poles,Weights,Knots,Mults,
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k,&m,NewPoles,NewWeights,nk,nm,Epsilon(U));
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}
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//=======================================================================
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//function : RaiseMultiplicity
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//purpose :
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//=======================================================================
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void BSplCLib::RaiseMultiplicity(const Standard_Integer KnotIndex,
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const Standard_Integer Mult,
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const Standard_Integer Degree,
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const Standard_Boolean Periodic,
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const Array1OfPoints& Poles,
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const TColStd_Array1OfReal* Weights,
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const TColStd_Array1OfReal& Knots,
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const TColStd_Array1OfInteger& Mults,
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Array1OfPoints& NewPoles,
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TColStd_Array1OfReal* NewWeights)
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{
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TColStd_Array1OfReal k(1,1);
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k(1) = Knots(KnotIndex);
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TColStd_Array1OfInteger m(1,1);
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m(1) = Mult - Mults(KnotIndex);
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TColStd_Array1OfReal nk(1,Knots.Length());
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TColStd_Array1OfInteger nm(1,Knots.Length());
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InsertKnots(Degree,Periodic,Poles,Weights,Knots,Mults,
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k,&m,NewPoles,NewWeights,nk,nm,Epsilon(k(1)));
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}
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//=======================================================================
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//function : IncreaseDegree
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//purpose :
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//=======================================================================
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void BSplCLib::IncreaseDegree
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(const Standard_Integer Degree,
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const Standard_Integer NewDegree,
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const Standard_Boolean Periodic,
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const Array1OfPoints& Poles,
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const TColStd_Array1OfReal* Weights,
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const TColStd_Array1OfReal& Knots,
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const TColStd_Array1OfInteger& Mults,
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Array1OfPoints& NewPoles,
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TColStd_Array1OfReal* NewWeights,
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TColStd_Array1OfReal& NewKnots,
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TColStd_Array1OfInteger& NewMults)
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{
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Standard_Boolean rational = Weights != NULL;
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Standard_Integer dim;
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dim = Dimension_gen;
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if (rational) dim++;
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TColStd_Array1OfReal poles(1,dim*Poles.Length());
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TColStd_Array1OfReal newpoles(1,dim*NewPoles.Length());
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if (rational) PLib::SetPoles(Poles,*Weights,poles);
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else PLib::SetPoles(Poles,poles);
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IncreaseDegree(Degree,NewDegree,Periodic,dim,poles,Knots,Mults,
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newpoles,NewKnots,NewMults);
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if (rational) PLib::GetPoles(newpoles,NewPoles,*NewWeights);
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else PLib::GetPoles(newpoles,NewPoles);
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}
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//=======================================================================
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//function : Unperiodize
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//purpose :
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//=======================================================================
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void BSplCLib::Unperiodize
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(const Standard_Integer Degree,
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const TColStd_Array1OfInteger& Mults,
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const TColStd_Array1OfReal& Knots,
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const Array1OfPoints& Poles,
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const TColStd_Array1OfReal* Weights,
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TColStd_Array1OfInteger& NewMults,
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TColStd_Array1OfReal& NewKnots,
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Array1OfPoints& NewPoles,
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TColStd_Array1OfReal* NewWeights)
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{
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Standard_Boolean rational = Weights != NULL;
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Standard_Integer dim;
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dim = Dimension_gen;
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if (rational) dim++;
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TColStd_Array1OfReal poles(1,dim*Poles.Length());
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TColStd_Array1OfReal newpoles(1,dim*NewPoles.Length());
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if (rational) PLib::SetPoles(Poles,*Weights,poles);
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else PLib::SetPoles(Poles,poles);
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Unperiodize(Degree, dim, Mults, Knots, poles,
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NewMults,NewKnots, newpoles);
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if (rational) PLib::GetPoles(newpoles,NewPoles,*NewWeights);
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else PLib::GetPoles(newpoles,NewPoles);
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}
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//=======================================================================
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//function : Trimming
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//purpose :
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//=======================================================================
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void BSplCLib::Trimming(const Standard_Integer Degree,
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const Standard_Boolean Periodic,
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const TColStd_Array1OfReal& Knots,
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const TColStd_Array1OfInteger& Mults,
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const Array1OfPoints& Poles,
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const TColStd_Array1OfReal* Weights,
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const Standard_Real U1,
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const Standard_Real U2,
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TColStd_Array1OfReal& NewKnots,
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TColStd_Array1OfInteger& NewMults,
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Array1OfPoints& NewPoles,
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TColStd_Array1OfReal* NewWeights)
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{
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Standard_Boolean rational = Weights != NULL;
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Standard_Integer dim;
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dim = Dimension_gen;
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if (rational) dim++;
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TColStd_Array1OfReal poles(1,dim*Poles.Length());
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TColStd_Array1OfReal newpoles(1,dim*NewPoles.Length());
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if (rational) PLib::SetPoles(Poles,*Weights,poles);
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else PLib::SetPoles(Poles,poles);
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Trimming(Degree, Periodic, dim, Knots, Mults, poles, U1, U2,
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NewKnots, NewMults, newpoles);
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if (rational) PLib::GetPoles(newpoles,NewPoles,*NewWeights);
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else PLib::GetPoles(newpoles,NewPoles);
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}
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//--------------------------------------------------------------------------
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//ELEMENTARY COMPUTATIONS
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//--------------------------------------------------------------------------
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//
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// All the following methods are methods of low level used in BSplCLib
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// but also in BSplSLib (but not in Geom)
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// At the creation time of this package there is no possibility
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// to declare private methods of package and to declare friend
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// methods of package. It could interesting to declare that BSplSLib
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// is a package friend to BSplCLib because it uses all the basis methods
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// of BSplCLib.
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//--------------------------------------------------------------------------
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//=======================================================================
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//function : BuildEval
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//purpose : builds the local array for evaluation
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//=======================================================================
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void BSplCLib::BuildEval(const Standard_Integer Degree,
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const Standard_Integer Index,
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const Array1OfPoints& Poles,
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const TColStd_Array1OfReal* Weights,
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Standard_Real& LP)
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{
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Standard_Real w, *pole = &LP;
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Standard_Integer PLower = Poles.Lower();
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Standard_Integer PUpper = Poles.Upper();
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Standard_Integer i;
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Standard_Integer ip = PLower + Index - 1;
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if (Weights == NULL) {
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for (i = 0; i <= Degree; i++) {
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ip++;
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if (ip > PUpper) ip = PLower;
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const Point& P = Poles(ip);
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PointToCoords (pole,P,+0);
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pole += Dimension_gen;
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}
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}
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else {
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for (i = 0; i <= Degree; i++) {
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ip++;
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if (ip > PUpper) ip = PLower;
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const Point& P = Poles(ip);
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pole[Dimension_gen] = w = (*Weights)(ip);
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PointToCoords (pole, P, * w);
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pole += Dimension_gen + 1;
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}
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}
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}
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//=======================================================================
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//function : PrepareEval
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//purpose : stores data for Eval in the local arrays
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// dc.poles and dc.knots
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//=======================================================================
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static void PrepareEval
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(Standard_Real& u,
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Standard_Integer& index,
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Standard_Integer& dim,
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Standard_Boolean& rational,
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const Standard_Integer Degree,
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const Standard_Boolean Periodic,
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const Array1OfPoints& Poles,
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const TColStd_Array1OfReal* Weights,
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const TColStd_Array1OfReal& Knots,
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const TColStd_Array1OfInteger* Mults,
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BSplCLib_DataContainer& dc)
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{
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// Set the Index
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BSplCLib::LocateParameter(Degree,Knots,Mults,u,Periodic,index,u);
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// make the knots
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BSplCLib::BuildKnots(Degree,index,Periodic,Knots,Mults,*dc.knots);
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if (Mults == NULL)
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index -= Knots.Lower() + Degree;
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else
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index = BSplCLib::PoleIndex(Degree,index,Periodic,*Mults);
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// check truly rational
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rational = (Weights != NULL);
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if (rational) {
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Standard_Integer WLower = Weights->Lower() + index;
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rational = BSplCLib::IsRational(*Weights, WLower, WLower + Degree);
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}
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// make the poles
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if (rational) {
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dim = Dimension_gen + 1;
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BSplCLib::BuildEval(Degree, index, Poles, Weights , *dc.poles);
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}
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else {
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dim = Dimension_gen;
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BSplCLib::BuildEval(Degree, index, Poles, BSplCLib::NoWeights(), *dc.poles);
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}
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}
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//=======================================================================
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//function : D0
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//purpose :
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//=======================================================================
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void BSplCLib::D0
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(const Standard_Real U,
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const Standard_Integer Index,
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const Standard_Integer Degree,
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const Standard_Boolean Periodic,
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const Array1OfPoints& Poles,
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const TColStd_Array1OfReal* Weights,
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const TColStd_Array1OfReal& Knots,
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const TColStd_Array1OfInteger* Mults,
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Point& P)
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{
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// Standard_Integer k,dim,index = Index;
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Standard_Integer dim,index = Index;
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Standard_Real u = U;
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Standard_Boolean rational;
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BSplCLib_DataContainer dc(Degree);
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PrepareEval(u,index,dim,rational,Degree,Periodic,Poles,Weights,Knots,Mults,dc);
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BSplCLib::Eval(u,Degree,*dc.knots,dim,*dc.poles);
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if (rational) {
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Standard_Real w = dc.poles[Dimension_gen];
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CoordsToPoint (P, dc.poles, / w);
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}
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else
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CoordsToPoint (P, dc.poles, );
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}
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//=======================================================================
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//function : D1
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//purpose :
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//=======================================================================
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void BSplCLib::D1
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(const Standard_Real U,
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const Standard_Integer Index,
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const Standard_Integer Degree,
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const Standard_Boolean Periodic,
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const Array1OfPoints& Poles,
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const TColStd_Array1OfReal* Weights,
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const TColStd_Array1OfReal& Knots,
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const TColStd_Array1OfInteger* Mults,
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Point& P,
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Vector& V)
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{
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Standard_Integer dim,index = Index;
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Standard_Real u = U;
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Standard_Boolean rational;
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BSplCLib_DataContainer dc(Degree);
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PrepareEval(u,index,dim,rational,Degree,Periodic,Poles,Weights,Knots,Mults,dc);
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BSplCLib::Bohm(u,Degree,1,*dc.knots,dim,*dc.poles);
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Standard_Real *result = dc.poles;
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if (rational) {
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PLib::RationalDerivative(Degree,1,Dimension_gen,*dc.poles,*dc.ders);
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result = dc.ders;
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}
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CoordsToPoint (P, result, );
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CoordsToPoint (V, result + Dimension_gen, );
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}
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//=======================================================================
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//function : D2
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//purpose :
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//=======================================================================
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void BSplCLib::D2
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(const Standard_Real U,
|
|
const Standard_Integer Index,
|
|
const Standard_Integer Degree,
|
|
const Standard_Boolean Periodic,
|
|
const Array1OfPoints& Poles,
|
|
const TColStd_Array1OfReal* Weights,
|
|
const TColStd_Array1OfReal& Knots,
|
|
const TColStd_Array1OfInteger* Mults,
|
|
Point& P,
|
|
Vector& V1,
|
|
Vector& V2)
|
|
{
|
|
Standard_Integer dim,index = Index;
|
|
Standard_Real u = U;
|
|
Standard_Boolean rational;
|
|
BSplCLib_DataContainer dc(Degree);
|
|
PrepareEval(u,index,dim,rational,Degree,Periodic,Poles,Weights,Knots,Mults,dc);
|
|
BSplCLib::Bohm(u,Degree,2,*dc.knots,dim,*dc.poles);
|
|
Standard_Real *result = dc.poles;
|
|
if (rational) {
|
|
PLib::RationalDerivative(Degree,2,Dimension_gen,*dc.poles,*dc.ders);
|
|
result = dc.ders;
|
|
}
|
|
|
|
CoordsToPoint (P, result, );
|
|
CoordsToPoint (V1, result + Dimension_gen, );
|
|
if (!rational && (Degree < 2))
|
|
NullifyPoint (V2);
|
|
else
|
|
CoordsToPoint (V2, result + 2 * Dimension_gen, );
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : D3
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void BSplCLib::D3
|
|
(const Standard_Real U,
|
|
const Standard_Integer Index,
|
|
const Standard_Integer Degree,
|
|
const Standard_Boolean Periodic,
|
|
const Array1OfPoints& Poles,
|
|
const TColStd_Array1OfReal* Weights,
|
|
const TColStd_Array1OfReal& Knots,
|
|
const TColStd_Array1OfInteger* Mults,
|
|
Point& P,
|
|
Vector& V1,
|
|
Vector& V2,
|
|
Vector& V3)
|
|
{
|
|
Standard_Integer dim,index = Index;
|
|
Standard_Real u = U;
|
|
Standard_Boolean rational;
|
|
BSplCLib_DataContainer dc(Degree);
|
|
PrepareEval(u,index,dim,rational,Degree,Periodic,Poles,Weights,Knots,Mults,dc);
|
|
BSplCLib::Bohm(u,Degree,3,*dc.knots,dim,*dc.poles);
|
|
Standard_Real *result = dc.poles;
|
|
if (rational) {
|
|
PLib::RationalDerivative(Degree,3,Dimension_gen,*dc.poles,*dc.ders);
|
|
result = dc.ders;
|
|
}
|
|
|
|
CoordsToPoint (P, result, );
|
|
CoordsToPoint (V1, result + Dimension_gen, );
|
|
if (!rational && (Degree < 2))
|
|
NullifyPoint (V2);
|
|
else
|
|
CoordsToPoint (V2, result + 2 * Dimension_gen, );
|
|
if (!rational && (Degree < 3))
|
|
NullifyPoint (V3);
|
|
else
|
|
CoordsToPoint (V3, result + 3 * Dimension_gen, );
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : DN
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void BSplCLib::DN
|
|
(const Standard_Real U,
|
|
const Standard_Integer N,
|
|
const Standard_Integer Index,
|
|
const Standard_Integer Degree,
|
|
const Standard_Boolean Periodic,
|
|
const Array1OfPoints& Poles,
|
|
const TColStd_Array1OfReal* Weights,
|
|
const TColStd_Array1OfReal& Knots,
|
|
const TColStd_Array1OfInteger* Mults,
|
|
Vector& VN)
|
|
{
|
|
Standard_Integer dim,index = Index;
|
|
Standard_Real u = U;
|
|
Standard_Boolean rational;
|
|
BSplCLib_DataContainer dc(Degree);
|
|
PrepareEval(u,index,dim,rational,Degree,Periodic,Poles,Weights,Knots,Mults,dc);
|
|
BSplCLib::Bohm(u,Degree,N,*dc.knots,dim,*dc.poles);
|
|
|
|
if (rational) {
|
|
Standard_Real v[Dimension_gen];
|
|
PLib::RationalDerivative(Degree,N,Dimension_gen,*dc.poles,v[0],Standard_False);
|
|
CoordsToPoint (VN, v, );
|
|
}
|
|
else {
|
|
if (N > Degree)
|
|
NullifyPoint (VN);
|
|
else {
|
|
Standard_Real *DN = dc.poles + N * Dimension_gen;
|
|
CoordsToPoint (VN, DN, );
|
|
}
|
|
}
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : Solves a LU factored Matrix
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
Standard_Integer
|
|
BSplCLib::SolveBandedSystem(const math_Matrix& Matrix,
|
|
const Standard_Integer UpperBandWidth,
|
|
const Standard_Integer LowerBandWidth,
|
|
Array1OfPoints& PolesArray)
|
|
{
|
|
Standard_Real *PArray ;
|
|
PArray = (Standard_Real *) &PolesArray(PolesArray.Lower()) ;
|
|
|
|
return BSplCLib::SolveBandedSystem(Matrix,
|
|
UpperBandWidth,
|
|
LowerBandWidth,
|
|
Dimension_gen,
|
|
PArray[0]) ;
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : Solves a LU factored Matrix
|
|
//purpose : if HomogeneousFlag is 1 then the input and the output
|
|
// will be homogeneous that is no division or multiplication
|
|
// by weigths will happen. On the contrary if HomogeneousFlag
|
|
// is 0 then the poles will be multiplied first by the weights
|
|
// and after interpolation they will be devided by the weights
|
|
//=======================================================================
|
|
|
|
Standard_Integer
|
|
BSplCLib::SolveBandedSystem(const math_Matrix& Matrix,
|
|
const Standard_Integer UpperBandWidth,
|
|
const Standard_Integer LowerBandWidth,
|
|
const Standard_Boolean HomogeneousFlag,
|
|
Array1OfPoints& PolesArray,
|
|
TColStd_Array1OfReal& WeightsArray)
|
|
{
|
|
Standard_Real *PArray,
|
|
* WArray ;
|
|
PArray = (Standard_Real *) &PolesArray(PolesArray.Lower()) ;
|
|
WArray = (Standard_Real *) &WeightsArray(WeightsArray.Lower()) ;
|
|
return BSplCLib::SolveBandedSystem(Matrix,
|
|
UpperBandWidth,
|
|
LowerBandWidth,
|
|
HomogeneousFlag,
|
|
Dimension_gen,
|
|
PArray[0],
|
|
WArray[0]) ;
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : Evaluates a Bspline function : uses the ExtrapMode
|
|
//purpose : the function is extrapolated using the Taylor expansion
|
|
// of degree ExtrapMode[0] to the left and the Taylor
|
|
// expansion of degree ExtrapMode[1] to the right
|
|
// if the HomogeneousFlag == True than the Poles are supposed
|
|
// to be stored homogeneously and the result will also be homogeneous
|
|
// Valid only if Weights
|
|
//=======================================================================
|
|
void BSplCLib::Eval(const Standard_Real Parameter,
|
|
const Standard_Boolean PeriodicFlag,
|
|
const Standard_Boolean HomogeneousFlag,
|
|
Standard_Integer& ExtrapMode,
|
|
const Standard_Integer Degree,
|
|
const TColStd_Array1OfReal& FlatKnots,
|
|
const Array1OfPoints& PolesArray,
|
|
const TColStd_Array1OfReal& WeightsArray,
|
|
Point& aPoint,
|
|
Standard_Real& aWeight)
|
|
{
|
|
Standard_Real Inverse,
|
|
P[Dimension_gen],
|
|
*PArray,
|
|
*WArray ;
|
|
Standard_Integer kk ;
|
|
PArray = (Standard_Real *) &PolesArray(PolesArray.Lower()) ;
|
|
WArray = (Standard_Real *) &WeightsArray(WeightsArray.Lower()) ;
|
|
if (HomogeneousFlag) {
|
|
BSplCLib::Eval(Parameter,
|
|
PeriodicFlag,
|
|
0,
|
|
ExtrapMode,
|
|
Degree,
|
|
FlatKnots,
|
|
Dimension_gen,
|
|
PArray[0],
|
|
P[0]) ;
|
|
BSplCLib::Eval(Parameter,
|
|
PeriodicFlag,
|
|
0,
|
|
ExtrapMode,
|
|
Degree,
|
|
FlatKnots,
|
|
1,
|
|
WArray[0],
|
|
aWeight) ;
|
|
}
|
|
else {
|
|
BSplCLib::Eval(Parameter,
|
|
PeriodicFlag,
|
|
0,
|
|
ExtrapMode,
|
|
Degree,
|
|
FlatKnots,
|
|
Dimension_gen,
|
|
PArray[0],
|
|
WArray[0],
|
|
P[0],
|
|
aWeight) ;
|
|
Inverse = 1.0e0 / aWeight ;
|
|
|
|
for (kk = 0 ; kk < Dimension_gen ; kk++) {
|
|
P[kk] *= Inverse ;
|
|
}
|
|
}
|
|
|
|
for (kk = 0 ; kk < Dimension_gen ; kk++)
|
|
aPoint.SetCoord(kk + 1, P[kk]) ;
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : CacheD0
|
|
//purpose : Evaluates the polynomial cache of the Bspline Curve
|
|
//
|
|
//=======================================================================
|
|
void BSplCLib::CacheD0(const Standard_Real Parameter,
|
|
const Standard_Integer Degree,
|
|
const Standard_Real CacheParameter,
|
|
const Standard_Real SpanLenght,
|
|
const Array1OfPoints& PolesArray,
|
|
const TColStd_Array1OfReal* WeightsArray,
|
|
Point& aPoint)
|
|
{
|
|
//
|
|
// the CacheParameter is where the cache polynomial was evaluated in homogeneous
|
|
// form
|
|
// the SpanLenght is the normalizing factor so that the polynomial is between
|
|
// 0 and 1
|
|
Standard_Real NewParameter, Inverse;
|
|
Standard_Real * PArray = (Standard_Real *) &(PolesArray(PolesArray.Lower())) ;
|
|
Standard_Real * myPoint = (Standard_Real *) &aPoint ;
|
|
NewParameter = (Parameter - CacheParameter) / SpanLenght ;
|
|
PLib::NoDerivativeEvalPolynomial(NewParameter,
|
|
Degree,
|
|
Dimension_gen,
|
|
Degree * Dimension_gen,
|
|
PArray[0],
|
|
myPoint[0]) ;
|
|
if (WeightsArray != NULL) {
|
|
const TColStd_Array1OfReal& refWeights = *WeightsArray;
|
|
Standard_Real *
|
|
WArray = (Standard_Real *) &refWeights(refWeights.Lower()) ;
|
|
PLib::NoDerivativeEvalPolynomial(NewParameter,
|
|
Degree,
|
|
1,
|
|
Degree,
|
|
WArray[0],
|
|
Inverse) ;
|
|
|
|
Inverse = 1.0e0 / Inverse;
|
|
ModifyCoords (myPoint, *= Inverse);
|
|
}
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : CacheD1
|
|
//purpose : Evaluates the polynomial cache of the Bspline Curve
|
|
//
|
|
//=======================================================================
|
|
void BSplCLib::CacheD1(const Standard_Real Parameter,
|
|
const Standard_Integer Degree,
|
|
const Standard_Real CacheParameter,
|
|
const Standard_Real SpanLenght,
|
|
const Array1OfPoints& PolesArray,
|
|
const TColStd_Array1OfReal* WeightsArray,
|
|
Point& aPoint,
|
|
Vector& aVector)
|
|
{
|
|
//
|
|
// the CacheParameter is where the cache polynomial was evaluated in homogeneous
|
|
// form
|
|
// the SpanLenght is the normalizing factor so that the polynomial is between
|
|
// 0 and 1
|
|
Standard_Real LocalPDerivatives[Dimension_gen << 1] ;
|
|
// Standard_Real LocalWDerivatives[2], NewParameter, Inverse ;
|
|
Standard_Real LocalWDerivatives[2], NewParameter ;
|
|
|
|
Standard_Real *
|
|
PArray = (Standard_Real *) &(PolesArray(PolesArray.Lower())) ;
|
|
Standard_Real *
|
|
myPoint = (Standard_Real *) &aPoint ;
|
|
Standard_Real *
|
|
myVector = (Standard_Real *) &aVector ;
|
|
NewParameter = (Parameter - CacheParameter) / SpanLenght ;
|
|
PLib::EvalPolynomial(NewParameter,
|
|
1,
|
|
Degree,
|
|
Dimension_gen,
|
|
PArray[0],
|
|
LocalPDerivatives[0]) ;
|
|
//
|
|
// unormalize derivatives since those are computed normalized
|
|
//
|
|
|
|
ModifyCoords (LocalPDerivatives + Dimension_gen, /= SpanLenght);
|
|
|
|
if (WeightsArray != NULL) {
|
|
const TColStd_Array1OfReal& refWeights = *WeightsArray;
|
|
Standard_Real *
|
|
WArray = (Standard_Real *) &refWeights(refWeights.Lower()) ;
|
|
PLib::EvalPolynomial(NewParameter,
|
|
1,
|
|
Degree,
|
|
1,
|
|
WArray[0],
|
|
LocalWDerivatives[0]) ;
|
|
//
|
|
// unormalize the result since the polynomial stored in the cache
|
|
// is normalized between 0 and 1
|
|
//
|
|
LocalWDerivatives[1] /= SpanLenght ;
|
|
|
|
PLib::RationalDerivatives(1,
|
|
Dimension_gen,
|
|
LocalPDerivatives[0],
|
|
LocalWDerivatives[0],
|
|
LocalPDerivatives[0]) ;
|
|
}
|
|
|
|
CopyCoords (myPoint, LocalPDerivatives);
|
|
CopyCoords (myVector, LocalPDerivatives + Dimension_gen);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : CacheD2
|
|
//purpose : Evaluates the polynomial cache of the Bspline Curve
|
|
//
|
|
//=======================================================================
|
|
void BSplCLib::CacheD2(const Standard_Real Parameter,
|
|
const Standard_Integer Degree,
|
|
const Standard_Real CacheParameter,
|
|
const Standard_Real SpanLenght,
|
|
const Array1OfPoints& PolesArray,
|
|
const TColStd_Array1OfReal* WeightsArray,
|
|
Point& aPoint,
|
|
Vector& aVector1,
|
|
Vector& aVector2)
|
|
{
|
|
//
|
|
// the CacheParameter is where the cache polynomial was evaluated in homogeneous
|
|
// form
|
|
// the SpanLenght is the normalizing factor so that the polynomial is between
|
|
// 0 and 1
|
|
Standard_Integer ii,Index,EndIndex;
|
|
Standard_Real LocalPDerivatives[(Dimension_gen << 1) + Dimension_gen] ;
|
|
// Standard_Real LocalWDerivatives[3], NewParameter, Factor, Inverse ;
|
|
Standard_Real LocalWDerivatives[3], NewParameter, Factor ;
|
|
Standard_Real * PArray = (Standard_Real *) &(PolesArray(PolesArray.Lower())) ;
|
|
Standard_Real * myPoint = (Standard_Real *) &aPoint ;
|
|
Standard_Real * myVector1 = (Standard_Real *) &aVector1 ;
|
|
Standard_Real * myVector2 = (Standard_Real *) &aVector2 ;
|
|
NewParameter = (Parameter - CacheParameter) / SpanLenght ;
|
|
PLib::EvalPolynomial(NewParameter,
|
|
2,
|
|
Degree,
|
|
Dimension_gen,
|
|
PArray[0],
|
|
LocalPDerivatives[0]) ;
|
|
//
|
|
// unormalize derivatives since those are computed normalized
|
|
//
|
|
Factor = 1.0e0/ SpanLenght ;
|
|
Index = Dimension_gen ;
|
|
EndIndex = Min (2, Degree) ;
|
|
|
|
for (ii = 1 ; ii <= EndIndex ; ii++) {
|
|
ModifyCoords (LocalPDerivatives + Index, *= Factor);
|
|
Factor /= SpanLenght ;
|
|
Index += Dimension_gen;
|
|
}
|
|
|
|
Index = (Degree + 1) * Dimension_gen;
|
|
for (ii = Degree ; ii < 2 ; ii++) {
|
|
NullifyCoords (LocalPDerivatives + Index);
|
|
Index += Dimension_gen;
|
|
}
|
|
|
|
if (WeightsArray != NULL) {
|
|
const TColStd_Array1OfReal& refWeights = *WeightsArray;
|
|
Standard_Real *
|
|
WArray = (Standard_Real *) &refWeights(refWeights.Lower()) ;
|
|
|
|
PLib::EvalPolynomial(NewParameter,
|
|
2,
|
|
Degree,
|
|
1,
|
|
WArray[0],
|
|
LocalWDerivatives[0]) ;
|
|
|
|
for (ii = Degree + 1 ; ii <= 2 ; ii++) {
|
|
LocalWDerivatives[ii] = 0.0e0 ;
|
|
}
|
|
//
|
|
// unormalize the result since the polynomial stored in the cache
|
|
// is normalized between 0 and 1
|
|
//
|
|
Factor = 1.0e0 / SpanLenght ;
|
|
|
|
for (ii = 1 ; ii <= EndIndex ; ii++) {
|
|
LocalWDerivatives[ii] *= Factor ;
|
|
Factor /= SpanLenght ;
|
|
}
|
|
PLib::RationalDerivatives(2,
|
|
Dimension_gen,
|
|
LocalPDerivatives[0],
|
|
LocalWDerivatives[0],
|
|
LocalPDerivatives[0]) ;
|
|
}
|
|
|
|
CopyCoords (myPoint, LocalPDerivatives);
|
|
CopyCoords (myVector1, LocalPDerivatives + Dimension_gen);
|
|
CopyCoords (myVector2, LocalPDerivatives + Dimension_gen * 2);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : CacheD3
|
|
//purpose : Evaluates the polynomial cache of the Bspline Curve
|
|
//
|
|
//=======================================================================
|
|
void BSplCLib::CacheD3(const Standard_Real Parameter,
|
|
const Standard_Integer Degree,
|
|
const Standard_Real CacheParameter,
|
|
const Standard_Real SpanLenght,
|
|
const Array1OfPoints& PolesArray,
|
|
const TColStd_Array1OfReal* WeightsArray,
|
|
Point& aPoint,
|
|
Vector& aVector1,
|
|
Vector& aVector2,
|
|
Vector& aVector3)
|
|
{
|
|
//
|
|
// the CacheParameter is where the cache polynomial was evaluated in homogeneous
|
|
// form
|
|
// the SpanLenght is the normalizing factor so that the polynomial is between
|
|
// 0 and 1
|
|
Standard_Integer ii, Index, EndIndex;
|
|
Standard_Real LocalPDerivatives[Dimension_gen << 2] ;
|
|
// Standard_Real LocalWDerivatives[4], Factor, NewParameter, Inverse ;
|
|
Standard_Real LocalWDerivatives[4], Factor, NewParameter ;
|
|
Standard_Real * PArray = (Standard_Real *) &(PolesArray(PolesArray.Lower())) ;
|
|
Standard_Real * myPoint = (Standard_Real *) &aPoint ;
|
|
Standard_Real * myVector1 = (Standard_Real *) &aVector1 ;
|
|
Standard_Real * myVector2 = (Standard_Real *) &aVector2 ;
|
|
Standard_Real * myVector3 = (Standard_Real *) &aVector3 ;
|
|
NewParameter = (Parameter - CacheParameter) / SpanLenght ;
|
|
PLib::EvalPolynomial(NewParameter,
|
|
3,
|
|
Degree,
|
|
Dimension_gen,
|
|
PArray[0],
|
|
LocalPDerivatives[0]) ;
|
|
|
|
Index = (Degree + 1) * Dimension_gen;
|
|
for (ii = Degree ; ii < 3 ; ii++) {
|
|
NullifyCoords (LocalPDerivatives + Index);
|
|
Index += Dimension_gen;
|
|
}
|
|
|
|
//
|
|
// unormalize derivatives since those are computed normalized
|
|
//
|
|
Factor = 1.0e0 / SpanLenght ;
|
|
Index = Dimension_gen ;
|
|
EndIndex = Min(3,Degree) ;
|
|
|
|
for (ii = 1 ; ii <= EndIndex ; ii++) {
|
|
ModifyCoords (LocalPDerivatives + Index, *= Factor);
|
|
Factor /= SpanLenght;
|
|
Index += Dimension_gen;
|
|
}
|
|
|
|
if (WeightsArray != NULL) {
|
|
const TColStd_Array1OfReal& refWeights = *WeightsArray;
|
|
Standard_Real *
|
|
WArray = (Standard_Real *) &refWeights(refWeights.Lower()) ;
|
|
|
|
PLib::EvalPolynomial(NewParameter,
|
|
3,
|
|
Degree,
|
|
1,
|
|
WArray[0],
|
|
LocalWDerivatives[0]) ;
|
|
//
|
|
// unormalize the result since the polynomial stored in the cache
|
|
// is normalized between 0 and 1
|
|
//
|
|
Factor = 1.0e0 / SpanLenght ;
|
|
|
|
for (ii = 1 ; ii <= EndIndex ; ii++) {
|
|
LocalWDerivatives[ii] *= Factor ;
|
|
Factor /= SpanLenght ;
|
|
}
|
|
|
|
for (ii = (Degree + 1) ; ii <= 3 ; ii++) {
|
|
LocalWDerivatives[ii] = 0.0e0 ;
|
|
}
|
|
PLib::RationalDerivatives(3,
|
|
Dimension_gen,
|
|
LocalPDerivatives[0],
|
|
LocalWDerivatives[0],
|
|
LocalPDerivatives[0]) ;
|
|
}
|
|
|
|
CopyCoords (myPoint, LocalPDerivatives);
|
|
CopyCoords (myVector1, LocalPDerivatives + Dimension_gen);
|
|
CopyCoords (myVector2, LocalPDerivatives + Dimension_gen * 2);
|
|
CopyCoords (myVector3, LocalPDerivatives + Dimension_gen * 3);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : BuildCache
|
|
//purpose : Stores theTaylor expansion normalized between 0,1 in the
|
|
// Cache : in case of a rational function the Poles are
|
|
// stored in homogeneous form
|
|
//=======================================================================
|
|
|
|
void BSplCLib::BuildCache
|
|
(const Standard_Real U,
|
|
const Standard_Real SpanDomain,
|
|
const Standard_Boolean Periodic,
|
|
const Standard_Integer Degree,
|
|
const TColStd_Array1OfReal& FlatKnots,
|
|
const Array1OfPoints& Poles,
|
|
const TColStd_Array1OfReal* Weights,
|
|
Array1OfPoints& CachePoles,
|
|
TColStd_Array1OfReal* CacheWeights)
|
|
{
|
|
Standard_Integer ii,
|
|
Dimension,
|
|
LocalIndex,
|
|
index = 0 ;
|
|
Standard_Real u = U,
|
|
LocalValue ;
|
|
Standard_Boolean rational;
|
|
|
|
BSplCLib_DataContainer dc(Degree);
|
|
PrepareEval(u,
|
|
index,
|
|
Dimension,
|
|
rational,
|
|
Degree,
|
|
Periodic,
|
|
Poles,
|
|
Weights,
|
|
FlatKnots,
|
|
(BSplCLib::NoMults()),
|
|
dc);
|
|
//
|
|
// Watch out : PrepareEval checks if locally the Bspline is polynomial
|
|
// therefore rational flag could be set to False even if there are
|
|
// Weights. The Dimension is set accordingly.
|
|
//
|
|
|
|
BSplCLib::Bohm(u,Degree,Degree,*dc.knots,Dimension,*dc.poles);
|
|
|
|
LocalValue = 1.0e0 ;
|
|
LocalIndex = 0 ;
|
|
|
|
if (rational) {
|
|
|
|
for (ii = 1 ; ii <= Degree + 1 ; ii++) {
|
|
CoordsToPoint (CachePoles(ii), dc.poles + LocalIndex, * LocalValue);
|
|
LocalIndex += Dimension_gen + 1;
|
|
LocalValue *= SpanDomain / (Standard_Real) ii ;
|
|
}
|
|
|
|
LocalIndex = Dimension_gen;
|
|
LocalValue = 1.0e0 ;
|
|
for (ii = 1 ; ii <= Degree + 1 ; ii++) {
|
|
(*CacheWeights)(ii) = dc.poles[LocalIndex] * LocalValue ;
|
|
LocalIndex += Dimension_gen + 1;
|
|
LocalValue *= SpanDomain / (Standard_Real) ii ;
|
|
}
|
|
}
|
|
else {
|
|
|
|
for (ii = 1 ; ii <= Degree + 1 ; ii++) {
|
|
CoordsToPoint (CachePoles(ii), dc.poles + LocalIndex, * LocalValue);
|
|
LocalIndex += Dimension_gen;
|
|
LocalValue *= SpanDomain / (Standard_Real) ii ;
|
|
}
|
|
|
|
if (Weights != NULL) {
|
|
for (ii = 1 ; ii <= Degree + 1 ; ii++)
|
|
(*CacheWeights)(ii) = 0.0e0 ;
|
|
(*CacheWeights)(1) = 1.0e0 ;
|
|
}
|
|
}
|
|
}
|
|
|
|
void BSplCLib::BuildCache(const Standard_Real theParameter,
|
|
const Standard_Real theSpanDomain,
|
|
const Standard_Boolean thePeriodicFlag,
|
|
const Standard_Integer theDegree,
|
|
const Standard_Integer theSpanIndex,
|
|
const TColStd_Array1OfReal& theFlatKnots,
|
|
const Array1OfPoints& thePoles,
|
|
const TColStd_Array1OfReal* theWeights,
|
|
TColStd_Array2OfReal& theCacheArray)
|
|
{
|
|
Standard_Real aParam = theParameter;
|
|
Standard_Integer anIndex = theSpanIndex;
|
|
Standard_Integer aDimension;
|
|
Standard_Boolean isRational;
|
|
|
|
BSplCLib_DataContainer dc(theDegree);
|
|
PrepareEval(aParam,
|
|
anIndex,
|
|
aDimension,
|
|
isRational,
|
|
theDegree,
|
|
thePeriodicFlag,
|
|
thePoles,
|
|
theWeights,
|
|
theFlatKnots,
|
|
(BSplCLib::NoMults()),
|
|
dc);
|
|
//
|
|
// Watch out : PrepareEval checks if locally the Bspline is polynomial
|
|
// therefore rational flag could be set to False even if there are
|
|
// Weights. The Dimension is set accordingly.
|
|
//
|
|
|
|
Standard_Integer aCacheShift = // helps to store weights when PrepareEval did not found that the curve is locally polynomial
|
|
(theWeights != NULL && !isRational) ? aDimension + 1 : aDimension;
|
|
|
|
BSplCLib::Bohm(aParam, theDegree, theDegree, *dc.knots, aDimension, *dc.poles);
|
|
|
|
Standard_Real aCoeff = 1.0;
|
|
Standard_Real* aCache = (Standard_Real *) &(theCacheArray(theCacheArray.LowerRow(), theCacheArray.LowerCol()));
|
|
Standard_Real* aPolyCoeffs = dc.poles;
|
|
|
|
for (Standard_Integer i = 0; i <= theDegree; i++)
|
|
{
|
|
for (Standard_Integer j = 0; j< aDimension; j++)
|
|
aCache[j] = aPolyCoeffs[j] * aCoeff;
|
|
aCoeff *= theSpanDomain / (i+1);
|
|
aPolyCoeffs += aDimension;
|
|
aCache += aDimension;
|
|
if (aCacheShift > aDimension)
|
|
{
|
|
aCache[0] = 0.0;
|
|
aCache++;
|
|
}
|
|
}
|
|
|
|
if (aCacheShift > aDimension)
|
|
theCacheArray.SetValue(theCacheArray.LowerRow(), theCacheArray.LowerCol() + aCacheShift - 1, 1.0);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : Interpolate
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void BSplCLib::Interpolate(const Standard_Integer Degree,
|
|
const TColStd_Array1OfReal& FlatKnots,
|
|
const TColStd_Array1OfReal& Parameters,
|
|
const TColStd_Array1OfInteger& ContactOrderArray,
|
|
Array1OfPoints& Poles,
|
|
Standard_Integer& InversionProblem)
|
|
|
|
{
|
|
Standard_Real *PArray ;
|
|
|
|
PArray = (Standard_Real *) &Poles(Poles.Lower()) ;
|
|
|
|
BSplCLib::Interpolate(Degree,
|
|
FlatKnots,
|
|
Parameters,
|
|
ContactOrderArray,
|
|
Dimension_gen,
|
|
PArray[0],
|
|
InversionProblem) ;
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : Interpolate
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void BSplCLib::Interpolate(const Standard_Integer Degree,
|
|
const TColStd_Array1OfReal& FlatKnots,
|
|
const TColStd_Array1OfReal& Parameters,
|
|
const TColStd_Array1OfInteger& ContactOrderArray,
|
|
Array1OfPoints& Poles,
|
|
TColStd_Array1OfReal& Weights,
|
|
Standard_Integer& InversionProblem)
|
|
{
|
|
Standard_Real *PArray,
|
|
* WArray ;
|
|
PArray = (Standard_Real *) &Poles(Poles.Lower()) ;
|
|
WArray = (Standard_Real *) &Weights(Weights.Lower()) ;
|
|
BSplCLib::Interpolate(Degree,
|
|
FlatKnots,
|
|
Parameters,
|
|
ContactOrderArray,
|
|
Dimension_gen,
|
|
PArray[0],
|
|
WArray[0],
|
|
InversionProblem) ;
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : MovePoint
|
|
//purpose : Find the new poles which allows an old point (with a
|
|
// given u as parameter) to reach a new position
|
|
//=======================================================================
|
|
|
|
void BSplCLib::MovePoint (const Standard_Real U,
|
|
const Vector& Displ,
|
|
const Standard_Integer Index1,
|
|
const Standard_Integer Index2,
|
|
const Standard_Integer Degree,
|
|
const Standard_Boolean Rational,
|
|
const Array1OfPoints& Poles,
|
|
const TColStd_Array1OfReal& Weights,
|
|
const TColStd_Array1OfReal& FlatKnots,
|
|
Standard_Integer& FirstIndex,
|
|
Standard_Integer& LastIndex,
|
|
Array1OfPoints& NewPoles)
|
|
{
|
|
// calculate the BSplineBasis in the parameter U
|
|
Standard_Integer FirstNonZeroBsplineIndex;
|
|
math_Matrix BSplineBasis(1, 1,
|
|
1, Degree+1);
|
|
Standard_Integer ErrorCode =
|
|
BSplCLib::EvalBsplineBasis(0,
|
|
Degree+1,
|
|
FlatKnots,
|
|
U,
|
|
FirstNonZeroBsplineIndex,
|
|
BSplineBasis);
|
|
if (ErrorCode != 0) {
|
|
FirstIndex = 0;
|
|
LastIndex = 0;
|
|
|
|
for (Standard_Integer i=Poles.Lower(); i<=Poles.Upper(); i++) {
|
|
NewPoles(i) = Poles(i);
|
|
}
|
|
return;
|
|
}
|
|
|
|
// find the span which is predominant for parameter U
|
|
FirstIndex = FirstNonZeroBsplineIndex;
|
|
LastIndex = FirstNonZeroBsplineIndex + Degree ;
|
|
if (FirstIndex < Index1) FirstIndex = Index1;
|
|
if (LastIndex > Index2) LastIndex = Index2;
|
|
|
|
Standard_Real maxValue = 0.0;
|
|
Standard_Integer i, kk1=0, kk2, ii;
|
|
|
|
for (i = FirstIndex-FirstNonZeroBsplineIndex+1;
|
|
i <= LastIndex-FirstNonZeroBsplineIndex+1; i++) {
|
|
if (BSplineBasis(1,i) > maxValue) {
|
|
kk1 = i + FirstNonZeroBsplineIndex - 1;
|
|
maxValue = BSplineBasis(1,i);
|
|
}
|
|
}
|
|
|
|
// find a kk2 if symetriy
|
|
kk2 = kk1;
|
|
i = kk1 - FirstNonZeroBsplineIndex + 2;
|
|
if ((kk1+1) <= LastIndex) {
|
|
if (Abs(BSplineBasis(1, kk1-FirstNonZeroBsplineIndex+2) - maxValue) < 1.e-10) {
|
|
kk2 = kk1+1;
|
|
}
|
|
}
|
|
|
|
// compute the vector of displacement
|
|
Standard_Real D1 = 0.0;
|
|
Standard_Real D2 = 0.0;
|
|
Standard_Real hN, Coef, Dval;
|
|
|
|
for (i = 1; i <= Degree+1; i++) {
|
|
ii = i + FirstNonZeroBsplineIndex - 1;
|
|
if (Rational) {
|
|
hN = Weights(ii)*BSplineBasis(1, i);
|
|
D2 += hN;
|
|
}
|
|
else {
|
|
hN = BSplineBasis(1, i);
|
|
}
|
|
if (ii >= FirstIndex && ii <= LastIndex) {
|
|
if (ii < kk1) {
|
|
Dval = kk1-ii;
|
|
}
|
|
else if (ii > kk2) {
|
|
Dval = ii - kk2;
|
|
}
|
|
else {
|
|
Dval = 0.0;
|
|
}
|
|
D1 += 1./(Dval + 1.) * hN;
|
|
}
|
|
}
|
|
|
|
if (Rational) {
|
|
Coef = D2/D1;
|
|
}
|
|
else {
|
|
Coef = 1./D1;
|
|
}
|
|
|
|
// compute the new poles
|
|
|
|
for (i=Poles.Lower(); i<=Poles.Upper(); i++) {
|
|
if (i >= FirstIndex && i <= LastIndex) {
|
|
if (i < kk1) {
|
|
Dval = kk1-i;
|
|
}
|
|
else if (i > kk2) {
|
|
Dval = i - kk2;
|
|
}
|
|
else {
|
|
Dval = 0.0;
|
|
}
|
|
NewPoles(i) = Poles(i).Translated((Coef/(Dval+1.))*Displ);
|
|
}
|
|
else {
|
|
NewPoles(i) = Poles(i);
|
|
}
|
|
}
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : MovePoint
|
|
//purpose : Find the new poles which allows an old point (with a
|
|
// given u as parameter) to reach a new position
|
|
//=======================================================================
|
|
|
|
//=======================================================================
|
|
//function : MovePointAndTangent
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void BSplCLib::MovePointAndTangent (const Standard_Real U,
|
|
const Vector& Delta,
|
|
const Vector& DeltaDerivatives,
|
|
const Standard_Real Tolerance,
|
|
const Standard_Integer Degree,
|
|
const Standard_Boolean Rational,
|
|
const Standard_Integer StartingCondition,
|
|
const Standard_Integer EndingCondition,
|
|
const Array1OfPoints& Poles,
|
|
const TColStd_Array1OfReal& Weights,
|
|
const TColStd_Array1OfReal& FlatKnots,
|
|
Array1OfPoints& NewPoles,
|
|
Standard_Integer & ErrorStatus)
|
|
{
|
|
Standard_Real *delta_array,
|
|
*delta_derivative_array,
|
|
*poles_array,
|
|
*new_poles_array ;
|
|
|
|
Standard_Integer num_poles ;
|
|
num_poles = Poles.Length() ;
|
|
|
|
if (NewPoles.Length() != num_poles) {
|
|
throw Standard_ConstructionError();
|
|
}
|
|
delta_array = (Standard_Real *) &Delta ;
|
|
delta_derivative_array = (Standard_Real *)&DeltaDerivatives ;
|
|
poles_array = (Standard_Real *) &Poles(Poles.Lower()) ;
|
|
|
|
new_poles_array = (Standard_Real *) &NewPoles(NewPoles.Lower()) ;
|
|
MovePointAndTangent(U,
|
|
Dimension_gen,
|
|
delta_array[0],
|
|
delta_derivative_array[0],
|
|
Tolerance,
|
|
Degree,
|
|
Rational,
|
|
StartingCondition,
|
|
EndingCondition,
|
|
poles_array[0],
|
|
Weights,
|
|
FlatKnots,
|
|
new_poles_array[0],
|
|
ErrorStatus) ;
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : Resolution
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void BSplCLib::Resolution(const Array1OfPoints& Poles,
|
|
const TColStd_Array1OfReal* Weights,
|
|
const Standard_Integer NumPoles,
|
|
const TColStd_Array1OfReal& FlatKnots,
|
|
const Standard_Integer Degree,
|
|
const Standard_Real Tolerance3D,
|
|
Standard_Real& UTolerance)
|
|
{
|
|
Standard_Real *PolesArray ;
|
|
PolesArray = (Standard_Real *) &Poles(Poles.Lower()) ;
|
|
BSplCLib::Resolution(PolesArray[0],
|
|
Dimension_gen,
|
|
NumPoles,
|
|
Weights,
|
|
FlatKnots,
|
|
Degree,
|
|
Tolerance3D,
|
|
UTolerance) ;
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : FunctionMultiply
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void BSplCLib::FunctionMultiply
|
|
(const BSplCLib_EvaluatorFunction & FunctionPtr,
|
|
const Standard_Integer BSplineDegree,
|
|
const TColStd_Array1OfReal & BSplineFlatKnots,
|
|
const Array1OfPoints & Poles,
|
|
const TColStd_Array1OfReal & FlatKnots,
|
|
const Standard_Integer NewDegree,
|
|
Array1OfPoints & NewPoles,
|
|
Standard_Integer & theStatus)
|
|
{
|
|
Standard_Integer num_bspline_poles =
|
|
BSplineFlatKnots.Length() - BSplineDegree - 1 ;
|
|
Standard_Integer num_new_poles =
|
|
FlatKnots.Length() - NewDegree - 1 ;
|
|
|
|
if (Poles.Length() != num_bspline_poles ||
|
|
NewPoles.Length() != num_new_poles) {
|
|
throw Standard_ConstructionError();
|
|
}
|
|
Standard_Real * array_of_poles =
|
|
(Standard_Real *) &Poles(Poles.Lower()) ;
|
|
Standard_Real * array_of_new_poles =
|
|
(Standard_Real *) &NewPoles(NewPoles.Lower()) ;
|
|
BSplCLib::FunctionMultiply(FunctionPtr,
|
|
BSplineDegree,
|
|
BSplineFlatKnots,
|
|
Dimension_gen,
|
|
array_of_poles[0],
|
|
FlatKnots,
|
|
NewDegree,
|
|
array_of_new_poles[0],
|
|
theStatus);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : FunctionReparameterise
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void BSplCLib::FunctionReparameterise
|
|
(const BSplCLib_EvaluatorFunction & FunctionPtr,
|
|
const Standard_Integer BSplineDegree,
|
|
const TColStd_Array1OfReal & BSplineFlatKnots,
|
|
const Array1OfPoints & Poles,
|
|
const TColStd_Array1OfReal & FlatKnots,
|
|
const Standard_Integer NewDegree,
|
|
Array1OfPoints & NewPoles,
|
|
Standard_Integer & theStatus)
|
|
{
|
|
Standard_Integer num_bspline_poles =
|
|
BSplineFlatKnots.Length() - BSplineDegree - 1 ;
|
|
Standard_Integer num_new_poles =
|
|
FlatKnots.Length() - NewDegree - 1 ;
|
|
|
|
if (Poles.Length() != num_bspline_poles ||
|
|
NewPoles.Length() != num_new_poles) {
|
|
throw Standard_ConstructionError();
|
|
}
|
|
Standard_Real * array_of_poles =
|
|
(Standard_Real *) &Poles(Poles.Lower()) ;
|
|
Standard_Real * array_of_new_poles =
|
|
(Standard_Real *) &NewPoles(NewPoles.Lower()) ;
|
|
BSplCLib::FunctionReparameterise(FunctionPtr,
|
|
BSplineDegree,
|
|
BSplineFlatKnots,
|
|
Dimension_gen,
|
|
array_of_poles[0],
|
|
FlatKnots,
|
|
NewDegree,
|
|
array_of_new_poles[0],
|
|
theStatus);
|
|
}
|